multiple issues expert November 2008 unreferenced November 2008 In mathematical field of geometric group theory , a length function is a function that assigns a number to each element of a group. Definition A length function L G &rarr R sup sup on a group mathematics group G is a function satisfying math begin align L e & 0, L g 1 & L g L g 1 g 2 & leq L g 1 L g 2 , quad forall g 1, g 2 in G. end align math Compare with the axioms for a Metric mathematics metric and a filtered algebra . Word metric main Word metric An important example of a length is the word metric given a presentation of a group by generators and relations, the length of an element is the length of the shortest word expressing it. Coxeter group s including the symmetric group have combinatorial important length functions, using the simple reflections as generators thus each simple reflection has length 1 . A longest element of a Coxeter group is both important and unique up to conjugation up to different choice of simple reflections . Properties A group with a length function does not form a filtered group , meaning that the sublevel set s math S i g mid ell g leq i math do not form subgroups in general. However, the group ring group algebra of a group with a length functions forms a filtered algebra the axiom math ell gh leq ell g ell h math corresponds to the filtration axiom. PlanetMath attribution id 4365 title Length function Category Group theory Category Geometric group theory ... more details
Feature length is List of motion picture terminology motion picture terminology referring to the length of a feature film . According to the rules of the Academy of Motion Picture Arts and Sciences , a feature length film motion picture must have a running time of more than 40 minutes to be eligible for an Academy Award . ref name oscars.org cite web url http www.oscars.org press pressreleases 2008 08.12.29.html title 281 Feature Films in Competitian for 2008 Oscar accessdate 2010 09 22 work Academy of Motion Picture Arts and Sciences publisher date ref The term may also be applied to non feature films with the minimum length, such as television film television movies and direct to video releases. Feature length can also be used to describe an episode of a television program TV series that has been extended to the length of a feature film. Such feature length episodes are usually television pilot series pilots , television special holiday specials or season finale s. History The earliest known feature length fictional film narrative film in the world was the Australian production The Story of the Kelly Gang 1906 , which was 60 minutes in length. Five reel Motion picture terminology reel features became common practice in the film industry industry in 1915. During the silent film silent era a one reel short film short ran for an average of 10 minutes, and a two reeler usually a comedy for 20 minutes, thus a feature was around 50 minutes or more. See also List of motion picture terminology Short film References reflist Category Film and video terminology film term stub ... more details
A horse length , or simply length , is a unit of measurement that refers to the length of a horse from nose to tail, approximately 8 feet, ref http www.drf.com help help glossary.html Daily Racing Form Glossary of Horse Racing Terms ref It is commonly used in Thoroughbred horse racing , where it describes the distance between horses in a race. Horses may be described as winning by several lengths, as in the notable example of Secretariat horse Secretariat , who won the Belmont Stakes by 31 lengths convert 248 ft m More often winning distances are merely a fraction of a length, such as half a length. Distances smaller than that are similarly described in reference to the equine body with terms such as a neck , a head , a short head , a nose or the slimmest fraction of a nose. These terms are used in other disciplines of equestrianism as well, particularly useful as a guide for riders in spacing animals apart when a number of them are all together in a riding arena , such as during group Riding academy riding instruction or at a horse show . Harness race finishing margins are typically measured in meters etc. See also Glossary of equestrian terms Glossary of Australian and New Zealand punting horse racing terms References reflist Category Horse racing Category Units of length ... more details
Refimprove date May 2011 Is the number of binary digits, called bit s, necessary to represent an integer ref cite web url http reference.wolfram.com mathematica ref BitLength.html title Wolfram Mathematica 8 Documentation accessdate 10 Jan 2012 ref in the binary numeral system binary number system . At their most fundamental level, digital computers and telecommunications devices as opposed to analog signal analog devices can process only data that has been expressed in binary code binary format. The binary format expresses data as an arbitrary length series of values with one of two choices Yes No, 1 0, True False, etc., all of which can be expressed electronically as On Off. For information technology applications, the amount of information being processed is an important design consideration. The term bit length is technical shorthand for this measure. For example, computer processors are often designed to process data group into data type word s of a given length of bits 8 bit, 16 bit, 32 bit, 64 bit, etc. . The bit length of each word data type word defines, for one thing, how many memory locations can be independently addressed by the processor. In public key cryptography , key cryptography key s are defined by their length expressed in binary digits their bit length. Reflist Category Binary arithmetic Category Computer arithmetic ... more details
For the cosmological notion of proper distance Comoving distance In relativistic physics, proper length is an invariant physics invariant measure of the distance between two spacelike separated Spacetime Basic concepts event s, or of the length of a spacelike Path topology path within a spacetime . The measurement of lengths is more complicated in the theory of relativity than in classical mechanics . In classical mechanics, lengths are measured based on the assumption that the locations of all points involved are measured simultaneously. But in the theory of relativity, the notion of Relativity of simultaneity simultaneity is dependent on the observer. Proper lengths provide an invariant measure, whose value is the same for all observers. Proper length is analogous to proper time . The difference is that proper length is the invariant spacetime interval interval of a spacelike path or pair of spacelike separated events, while proper time is the invariant interval of a timelike path or pair of timelike separated events. Proper length between two events In special relativity , the proper length between two spacelike separated events is the distance between the two events, as measured ... at opposite ends of an object, the proper length of the object is the length of the object as measured ... length L is math L sqrt Delta x 2 Delta y 2 Delta z 2 c 2 Delta t 2 math , where t is the difference ... zero value for L . Proper length of a path The above formula for the proper length between two events ..., possible to define the proper length of a Path topology path in any spacetime, curved or flat. In a flat spacetime, the proper length between two events is the proper length of a straight path between ... relativity geodesic between two events, so the proper length of a straight path between two events would not uniquely define the proper length between the two events. Along an arbitrary spacelike path P , the proper length is given in tensor syntax by the line integral math L c int P sqrt g mu nu dx ... more details
Orphan date February 2009 Expert subject physics date November 2008 Thermodynamic length is a Riemannian metric defined on a manifold of thermodynamic state s. Clarify date November 2008 Category Thermodynamics Physics stub ... more details
NOTOC For the measurement of an ammunition cartridge Overall length Image LOA LWL.svg thumb right 300px LOA Length Overall & LWL Waterline Length Image Ship length measurements.png thumb right 300px Detailed hull dimensions Length overall , often abbreviated as LOA , o a , o.a. or oa refers to the maximum length of a vessel from the two points on the hull measured perpendicular to the waterline. Length overall is commonly used to indicate maximum length of a vessel. LOA is the most commonly used way of expressing the size of a boat, and is also used for calculating the cost of a marina Berth moorings berth ref cite web url http www.mosquitocreekmarina.com moorage.html title Boat Moorage publisher Mosquito Creek Marina accessdate 2009 07 13 ref for example, 2.50 per metre LOA . As said, LOA often means length of the hull. ref cite web url http www.westlawn.edu student center definitions.asp title Definitions of Boat, Yacht, Small Craft, and Related Terms publisher Westlawn Institute of Marine ... http books.google.com ?id 9 7ycOuv6a4C&pg PA64&dq LOA length overall LOD donald title Dictionary ... ?id QgMRudqoLGQC&pg PR19&dq length overall unambiguously tons gross last Sch uffelen first ... publisher Wilh. Wilhelmsen ASA accessdate 2009 07 18 ref Sparred length , Total length including bowsprit , Mooring length and LOA including bowsprit are other expressions that might indicate the full length of a sailing ship. LOH In ISO 8666 for small boats, cited by a product description, ref ... International page 4 format PDF ref there is a definition of LOH, length of hull, ref cite ... 2009 07 18 ref that measures shorter than LOA. LWL Another measure of length is LWL loaded waterline length which is more useful in assessing a vessel s performance. In some cases particularly old yacht s or vessels with bowsprit s LWL can be considerably shorter than LOA. See also Overall length ... of Historic Vessels The National Register of Historic Vessels Length between perpendiculars References ... more details
For the measurement of a ship s lengthlength overall The overall length of an ammunition Cartridge firearms cartridge is a measurement from the base of the brass Shell projectile shell Casing ammunition casing to the tip of the bullet , seated into the brass casing. ref name COTW2009 cite book title Cartridges of the World A Complete and Illustrated Reference for Over 1500 Cartridges first Frank C. last Barnes coauthors Holt Bodinson, Layne Simpson edition 12 page 157 publisher Gun Digest Books year 2009 isbn 9780896899360 ref Handloaded cartridges and commercially available cartridges for firearm s are normally created with a maximum length standardized by the Sporting Arms and Ammunition Manufacturers Institute SAAMI . A cartridge s overall length may be shorter than the maximum standard, equal to the standard, or sometimes even longer. The maximum overall length is dictated by the need to fit into a box magazine of standard manufacture. For example, the .223 Remington cartridge, when loaded for use in the AR 15 rifle or the military s M16 rifle M 16 rifle , has to fit into the removable box magazine for that rifle. This dictates that the cartridge s maximum overall length be no greater than 2.260 . However, for competition purposes during off hand and slow fire prone match stages, the .223 Remington is loaded one cartridge at a time into the rifle s receiver. This allows for the cartridge to be longer than the standardized 2.260 SAAMI maximum overall length. These cartridges can be safely loaded to a length that has the ogive portion of the bullet just touching the rifle s lands. Many competitive shooters will make these cartridges 0.005 less than the truly maximum allowable overall length, for the sake of safety. ref name ABC cite book title The ABCs of Reloading The Definitive Guide for Novice to Expert first Rodney last James edition 9 page 127 publisher Krause Publications year 2011 isbn 9781440213960 ref It is desirable for these single loaded cartridges to have ... more details
Refimprove date December 2009 The Kuhn length is a theoretical treatment, developed by Werner Kuhn , in which a real polymer chain is considered as a collection of math N math Kuhn segments each with a Kuhn length math b math . Each Kuhn segment can be thought of as if they are freely jointed with each other. ref Flory, P.J. 1953 Principles of Polymer Chemistry , Cornell Univ. Press, ISBN 0 8014 0134 8 ref ref Flory, P.J. 1969 Statistical Mechanics of Chain Molecules , Wiley, ISBN 0 470 26495 0 reissued 1989, ISBN 1 56990 019 1 ref ref Rubinstein, M., Colby, R. H. 2003 Polymer Physics , Oxford University Press, ISBN 0 19 852059 X ref Each segment in a freely jointed chain can randomly orient in any direction without the influence of any forces, independent of the directions taken by other segments. Thus the real chain consisting of math n math bonds and with fixed bond angles and bond lengths is replaced by an equivalent chain with math N math connected Kuhn segments that can orient in any random direction. The length of a fully stretched chain or the contour length is math L Nb math for the Kuhn segment chain. In the simplest treatment, such a chain follows the random walk model, where each step taken in a random direction is independent of the directions taken in the previous steps, forming a random coil . The average end to end distance for a chain satisfying the random walk model is math R 2 Nb 2 math . Since the space occupied by a segment in the polymer chain cannot be taken ... homopolymer chain consists of the same repeat units with bond length math l math and bond angle ... cos textstyle phi , math is the average cosine of the dihedral angle. Also the fully stretched length ... length math b math can be obtained. File Molecule 1.jpg thumb Bond angle For worm like chain semiflexible chain , Kuhn length equals two times the persistence length ref Gert R. Strobl 2007 The physics ... ref . References Reflist DEFAULTSORT Kuhn Length Category Polymer chemistry Category Polymer physics ... more details
A cable length or cable s length is a nautical Units of measurement unit of measure equal to one tenth of a nautical mile or 100 fathoms , or sometimes 120 fathoms. The unit is named after the length of a ship s anchor cable in the age of sail . The definition varies International frac 10 nautical mile , or 185.2 metre m Imperial units Imperial Admiralty frac 10 Nautical mile Admiralty mile , or 608 ft 185.32 m , about 101 fathom s The traditional British fathom varied from 5 feet to 7 feet in the Merchant Navy . United States customary units U.S. customary US Navy 120 fathoms 720 feet, 219.456 m References citation author Fenna, Donald year 2002 contribution cable, cable length, cable s length title A Dictionary of Weights, Measures, and Units location Oxford publisher University Press isbn 0 19 860522 6 . Also fathom , from the same work. citation url http web.archive.org web 20080707042523 http www.royal navy.mod.uk server show nav.3807 content title Navy Slang Cable Curry publisher Royal Navy accessdate February 2011 . See also Conversion of units Category Units of length Category Nautical terms be x old cs Kabel jednotka de Kabell nge et Kaabeltau el es Cable unidad de longitud fr Encablure he hr Kabel mjera lv Kabe tauva mk nl Kabellengte ja no Kabellengde nn Kabellengd pl Kabel jednostka ru fi Kaapelinmitta sv Kabell ngd tr Gomina uk ... more details
The Richard Tolman Tolman length math delta math also known as Tolman s delta measures the extent by which the surface tension of a small liquid drop deviates from its planar value. It is conveniently defined in terms of an expansion in math 1 R math , with math R R e math the equimolar radius of the liquid drop, of the pressure difference across the droplet s surface center math Delta p frac 2 sigma R left 1 frac delta R ldots right math 1 center In this expression, math Delta p p l p v math is the pressure difference between the bulk pressure of the liquid inside and the pressure of the vapour outside, and math sigma math is the surface tension of the planar interface , i.e. the interface with zero curvature math R infty math . The Tolman length math delta math is thus defined as the leading order correction in an expansion in math 1 R math . Another way to define the tolman length is to consider the radius dependence of the surface tension, math sigma R math . To leading order in math 1 R math one has center math sigma R sigma left 1 frac 2 delta R ldots right math 2 center Here math ... length is defined as a coefficient in an expansion in math 1 R math and therefore does not depend on R. Furthermore, the Tolman length can be related to the radius of spontaneous curvature when ... center math delta sigma frac 2k R 0 math center Any result for the Tolman length therefore gives information about the radius of spontaneous curvature, math R 0 math . If the Tolman length is known ... length implies a negative math R 0 math and a preferred curvature towards the vapour phase. Apart from being related to the radius of spontaneous curvature, the Tolman length can also be linked to the surface ... of tension. Using the Gibbs adsorption equation , Tolman himself showed that the Tolman length can ... Gibbs Gibbs yields the value of the Tolman length center math delta lim R s rightarrow infty R e ... making the magnitude of the Tolman length in the order of nanometers. References R.C. Tolman, J ... more details
No footnotes date January 2010 In physics , the attenuation length or absorption length is the distance math lambda math into a material when the probability has dropped to math 1 e math that a Elementary particle particle has not been Absorption electromagnetic radiation absorbed . Alternatively, if there is a beam of particles incident on the material, the attenuation length is the distance where the intensity physics intensity of the beam has dropped to math 1 e math , or about 63 of the particles have been stopped. Mathematically, the probability of finding a particle at depth x into the material is calculated by Beer Lambert law math P x e x lambda , math . In general math lambda math is material dependent. See also Beer s Law Mean free path Attenuation coefficient Attenuation electromagnetic radiation Radiation length References S. Eidelman et al. Particle Data Group , Review of particle physics , Phys. Lett. B 592 2004 http pdg.lbl.gov http www.ct.infn.it rivel Glossario node2.html External links http henke.lbl.gov optical constants atten2.html Category Particle physics Category Experimental particle physics particle stub de Absorptionsl nge it Lunghezza di attenuazione ... more details
In mathematics , especially in the area of algebra known as group theory , the Fitting length or nilpotent length measures how far a solvable group is from being nilpotent group nilpotent . The concept is named after Hans Fitting , due to his investigations of nilpotent normal subgroups . Definition A Fitting chain or Fitting series or visible anchor nilpotent series for a group mathematics group is a subnormal series with nilpotent group nilpotent quotient group quotients . In other words, a finite sequence of subgroup s including both the whole group and the trivial group, such that each is a normal subgroup of the previous one, and such that the quotients of successive terms are nilpotent groups. The Fitting length or nilpotent length of a group mathematics group is defined to be the smallest possible length of a Fitting chain, if one exists. Upper and lower Fitting series Just as the upper central series and lower central series are extremal among central series , there are analogous series extremal among nilpotent series. For a finite group H , the Fitting subgroup Fit H is the maximal normal nilpotent subgroup, while the minimal subgroup such that the quotient by it is nilpotent is sub sub H , the intersection of the finite lower central series , which is called the nilpotent residual . These correspond to the center and the commutator subgroup for upper and lower central ... series, at each step taking the minimal possible subgroup. Examples A group has Fitting length ... Fitting length 2. The tetrahedral group symmetric group on four points has Fitting length 3. The symmetric ... product of n copies of the symmetric group on three points has Fitting length 2 n . Properties ... sup i sup G , and F sub i sub G H sub n i sub . For a solvable group, the length of the lower Fitting series is equal to length of the upper Fitting series, and this common length is the Fitting length ... length first Alexandre last Turull note the typos, Fitting height versus Fitting length springer ... more details
In physics , length contraction according to Hendrik Lorentz is the physical phenomenon of a decrease in length detected by an observer of objects that travel at any non zero velocity relative to that observer ... , the length is 99.9 of the length at rest at a speed of 42,300,000 m s 95 million mph, 0.141c , the length is still 99 . As the magnitude of the velocity approaches the speed of light, the effect ... where math L 0 math is the proper length the length of the object in its rest frame , math L math is the length ... in relative movement, the length of the object is measured by subtracting the simultaneously ... would observe the length of the object in the direction of motion as very near zero. History Main History of special relativity Length contraction was postulated by George Francis FitzGerald 1889 ... the hypothesis of the stationary aether Lorentz ether theory Length contraction Lorentz ... as of electromagnetic origin, and length contraction appeared to be a direct consequence of this model ... a dynamical explanation for length contraction. But this model was subject to the same problem as the original hypotheses Length contraction and the non electromagnetic forces were only invented ... that length contraction was no dynamical effect in the aether, but rather a kinematic effect due ... meaning of all relativistic effects in spacetime . So length contraction is not of Kinetics physics ... and the observed object is zero, then the proper length math L 0 math of the object can simply be determined ... was passing by at the same time . It s clear that distance AB is equal to length math L ... distant than those of A and C. Thus the definition of simultaneity is crucial for measuring the length ... . As the result of this transformation see Derivation , the proper length remains unchanged and always denotes the greatest length of an object, yet the length of the same object as measured in another inertial frame is shorter than the proper length. This contraction only occurs in the line of motion ... more details
Determining the length of an irregular arc segment is also called rectification of a curve . Historically ... to calculate the length of each linear segment using the Pythagorean theorem in Euclidean space, for example , the total length of the approximation can be found by summation summing ... arbitrarily small . For some curves there is a smallest number L that is an upper bound on the length ... and the curve is defined to have arc length L . Definition See also Curve Lengths of curves l1 Lengths ... is the length of the line segment connecting the two points. The arc length L of C is then defined to be math ... over all possible partitions of a , b and n is unbounded. The arc length L is either wiktionary .... This definition of arc length does not require that C be defined by a derivative differentiable ... a sum involving g can be made equal to a sum involving f. So the arc length is an intrinsic property ... of arc length for the curve is analogous to the definition of the total variation of a real valued function. Finding arc lengths by integrating See also Differential geometry of curves Length and natural ... continuous on a , b . The length s of the part of the graph of f between x a and x b can be found ... X t and y Y t , then its arc length between t a and t b is math s int a b sqrt X t 2 Y t 2 , dt. math ... length is given by math s int a b sqrt r 2 left frac dr d theta right 2 , d theta. math In most ... length and numerical integration is necessary. Curves with closed form solution for arc length ... length of an Ellipse Circumference elliptic arc led to the development of the elliptic integral s. Derivation ... Nowrap 1 y t sup 5 sup , x t sup 3 sup In order to approximate the arc length of the curve, it is split ... image and observe that its length element of the arc length will be the differential mathematics ..., math which is the arc length from x a to x b of the graph of the function . For example, the curve in this figure is defined by math begin cases y t 5, x t 3. end cases math Subsequently, the arc length ... more details
length for side slip defined by Pacejka is higher than the relaxation length determined from the steady state side force. accessdate 2010 10 31 ref The relaxation length assotiated with camber thrust has been found to be nearly zero. ref name Cossalter Importance A tire s relaxation length ... University of Technology pages 16 quote the relaxation length plays an important role in the shimmy ... more details
refimprove date December 2011 In telecommunications , electrical length is the length of a transmission medium or antenna electronics antenna element expressed as the number of wavelength s of the Signalling telecommunication signal propagating in the medium. Electromagnetic waves propagate more slowly in a medium than in free space, so a wave in a medium will have a larger number of waves than a wave of the same frequency propagating over the same distance in free space. Alternatively put, the distance ..., hence the transmission medium is said to have an electrical length greater than its physical length. The electrical length is most commonly expressed in units of the wavelength, , which is related ... v f math A length may be stated as 2 or 3 or 0.5 etc. It is also sometimes expressed in radian s or degree angle degrees . A length of can be converted to radians by math theta 2 pi nu , math ... space, and the electrical length approximately 1.5 times the physical length. Antennas Many antenna ... length be equal to a multiple of a half wavelength, 2, while for a monopole antenna it is a multiple of a quarter wavelength, 4. The electrical length of an antenna element is, in general, different from its physical length. For example, increasing the diameter of the conductor, or the presence ... length. Antennas which are the wrong length to be resonant, or which must operate at a different ... 1037C ref An antenna which is shorter than its resonant length has capacitive reactance . The capacitance ... its resonant length has inductive reactance , and can be electrically shortened by adding a loading ... of a suitable electronic device, without changing the physical length of the aerial, in such a way ... wavelength. Thus an aerial with a length corresponding to the eighth of the radiated wavelength can ... than about one half wave length of the frequency at which the antenna operates. These antennas may operate ... Dec 7, 1937 DEFAULTSORT Electrical Length Category Telecommunications Category Antennas de Elektrische ... more details
length of a collection of curve s math Gamma math is a conformal invariant of math Gamma ... length of math Gamma math is equal to the extremal length of the image of math Gamma math under math f math . For this reason, the extremal length is a useful tool in the study of conformal mappings. Extremal length can also be useful in dimensions greater than two, but the following deals primarily with the two dimensional setting. Definition of extremal length To define extremal length ... gamma math we let math L rho gamma int gamma rho , dz math denote the math rho math length of math gamma math , where math dz math denotes the Euclidean distance Euclidean element of length. It is possible ... the measure of every subinterval math J subset I math is the length of the restriction of math ... integral math int I rho gamma t ,d mathrm length gamma t math , where math mathrm length gamma t math is the length of the restriction of math gamma math to math s in I s le t math . Also set math ... int D rho 2 ,dx ,dy, math and the extremal length of math Gamma math is math EL Gamma sup rho frac ... length of the collection of curves in math D math with one endpoint in one set and the other endpoint in the other set. Examples In this section the extremal length is calculated in several examples. The first three of these examples are actually useful in applications of extremal length. Extremal ... math R 0,w times 0,h math . Let math Gamma math be the set of all finite length curves math gamma ... gamma math has finite length. We will now prove that in this case math EL Gamma w h math First .... As the proof shows, the extremal length of math Gamma math is the same as the extremal length ... length of the family of curves math Gamma , math that connect the bottom edge of math ... length, and a similar duality property occurs in the context of the next subsection. Observe ... 1 math and math C 2 math which is the extremal length of the collection math Gamma math of curves math ... more details
In physics, the radiation length is a characteristic of a material, related to the energy loss of high energy, electromagnetic interacting elementary particle particles with it. Definition High energy electrons 10 MeV predominantly lose energy in matter by bremsstrahlung , and high energy photons by SubatomicParticle Antielectron SubatomicParticle Electron pair production. The characteristic amount of matter traversed for these related interactions is called the radiation length math X sub 0 sub , usually measured in g cm sup 2 sup . It is both the mean distance over which a high energy electron loses all but math frac 1 e mathematical constant e of its energy by bremsstrahlung, and frac 7 9 of the mean free path for pair production by a high energy photon. It is also the appropriate scale length for describing high energy electromagnetic cascades. The radiation length for a given material consisting of a single type of nuclei can be approximated by the following expression ref cite book last Eidelman first S. title Review of Particle Physics ref math X 0 frac 716.4 cdot A Z Z 1 ln frac 287 sqrt Z mathrm g cdot mathrm cm 2 frac 1432.8 cdot A Z Z 1 11.319 ln Z mathrm g cdot mathrm cm 2 math , where math Z is the atomic number and math A is mass number of the nucleus. For electrons at lower energies below few tens of MeV s , the energy loss by ionization is predominant. While this definition may also be used for other electromagnetic interacting particles beyond lepton s and photons, the presence of the stronger strong interaction hadronic and Nuclear force nuclear interaction makes it a far less interesting characterisation of the material the nuclear collision length and nuclear interaction length are more relevant. Comprehensive tables for radiation lengths and other properties of materials are available from http pdg.lbl.gov AtomicNuclearProperties See also Mean free path Attenuation length Attenuation coefficient Attenuation Range particle radiation Stopping power ... more details
Length constant is a constant used in neurobiology signified by the Greek letter lambda &lambda . The longer a length constant is, the bigger the effect a potential either an action potential or a current injected at the site will have along the cell. A long length constant can result in spatial summation , or the algebraic summation of one potential with other potentials from other areas of the cell. In an action potential or in a passive spread of signal in a neuron , the constant &lambda is math lambda sqrt frac r m r i r o math where r sub m sub is the resistance across the membrane, r sub i sub is the resistance inside the membrane, and r sub o sub is the resistance outside the membrane. In calculation, the effects of r sub o sub are negligible, so the equation becomes math lambda sqrt frac r m r i math The resistance across the membrane is a function of the number of open ion channels and the resistance inside the membrane is generally a function of the diameter of the axon . A large diameter is related to a lower r sub i sub . The length constant is used to describe the rise of potential difference across the membrane math V x V max 1 e x lambda math The fall of voltage is described by math V x V max e x lambda math Where voltage is typically in millivolts, x is distance in millimeters, and &lambda is in millimeters. V sub max sub is defined as the maximum voltage attained in the action potential, where math V max r m I math where r sub m sub is the resistance across the membrane and I is the current flow. Setting for x &lambda for the rise of voltage sets V x equal to .63 V sub max sub . This means that the length constant is the distance at which 63 of V sub max sub has been reached during the rise of voltage. Setting for x &lambda for the fall of voltage sets V x equal to .37 V sub max sub , meaning that the length constant is the distance at which 37 of V sub ... in this way, it can be seen that the length constant increases with increasing radius of the neuron ... more details
s is related to the Rayleigh length by ref name Siegman1986 math Theta mathrm div 2 frac w 0 z R . math ... Depth of field References reflist http www.rp photonics.com rayleigh length.html Rayleigh length ... more details
The Bjerrum length after Danish chemist Niels Bjerrum 1879 1958 ref http www.rsc.org delivery ArticleLinking DisplayArticleForFree.cfm?doi TF959550X001&JournalCode TF ref is the separation at which the electrostatic interaction between two elementary charge s is comparable in magnitude to the thermal energy scale, math k B T math , where math k B math is the Boltzmann constant and math T math is the Absolute temperature absolute temperature in Kelvin . This length scale arises naturally in discussions of electrostatic, electrodynamic and electrokinetic phenomena in electrolytes, polyelectrolyte and colloidal dispersions. ref cite book last1 Russel first1 William B. first2 D. A. last2 Saville first3 William R. last3 Schowalter title Colloidal Dispersions publisher Cambridge University Press location New York year 1989 ref In SI units standard units , the Bjerrum length is given by math lambda B frac e 2 4 pi varepsilon 0 varepsilon r k B T , math where math e math is the elementary charge , math varepsilon r math is the relative dielectric constant of the medium and math varepsilon 0 math is the vacuum permittivity . For water at room temperature math T 300 mbox K math , math varepsilon r approx 80 math , so that math lambda B approx 0.7 math nm. In Gaussian units , math 4 pi varepsilon 0 1 math and the Bjerrum length has the simpler form math lambda B frac e 2 varepsilon r k B T . math References Reflist Category physical chemistry de Bjerrum L nge fa ... more details
Orphan date January 2011 The transport length in a strongly diffusing medium noted l is the length over which the direction of propagation of the photon is randomized. It is related to the mean free path l by the relation ref A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978. ref math l frac l 1 g math with g the asymmetry coefficient. math g cos theta math or averaging of the scattering angle over a high number of scattering events. g can be evaluated with the Mie theory . br If g 0, l l . A single scattering is already isotropic. br If g 1, l infinite. A single scattering doesn t deviate the photons. Then the scattering never gets isotropic. This length is useful for renormalizing a non isotropic scattering problem into an isotropic one in order to use classical diffusion laws Fick law and Brownian motion . The transport length might be measured by transmission experiments of backscattering experiments. ref Talanta, Volume 50, Issue 2, 13 September 1999, Pages 445 456 ref ref P. Snabre, A. Arhaliass, Anisotropic scattering of light in random media. Incoherent backscattered spot light, Appl. Optics 37 18 1998 211 225. ref gallery Image figure mean free path.png Mean free path simple scheme gallery References references External links http www.formulaction.com tech mls gb.html Illustrated description movies of multiple light scattering and application to colloid stability Category Optics Category Colloids ... more details
Infobox film name Length of War image caption director Gonzalo Mart nez Ortega producer writer Heriberto Frias br Gonzalo Mart nez Ortega starring V ctor Alcocer music cinematography Rosal o Solano editing distributor released Film date 1976 12 21 df yes runtime 142 minutes country film Mexico language Spanish budget Length of War lang es Longitud de guerra is a 1976 Mexican drama film directed by Gonzalo Mart nez Ortega . ref name cinemexicano cite web url http escritores.cinemexicano.unam.mx biografias M MARTINEZ ortega gonzalo biografia.html title Gonzalo Mart nez Ortega accessdate 2012 03 31 work cinemexicano ref The film was selected as the Mexican entry for the Academy Award for Best Foreign Language Film Best Foreign Language Film at the 49th Academy Awards , but was not accepted as a nominee. ref Margaret Herrick Library, Academy of Motion Picture Arts and Sciences ref Cast V ctor Alcocer Jos Luis Almada Mario Almada actor Mario Almada Pedro Armend riz Jr. Fernando Balzaretti Elsa Benn Narciso Busquets Roberto Ca edo Armando Coria Pancho C rdova Eugenia D Silva ngel de la Pe a Garc a Alma Delfina See also List of submissions to the 49th Academy Awards for Best Foreign Language Film List of Mexican submissions for the Academy Award for Best Foreign Language Film References reflist External links IMDb title 0218412 Length of War DEFAULTSORT Length Of War Category 1976 films Category Mexican films Category Spanish language films Category 1970s drama films Category Films directed by Gonzalo Mart nez Ortega 1970s Mexico film stub ... more details
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